JEE Advance - Mathematics (2005 - No. 21)
The value of $$$\left( {\matrix{
{30} \cr
0 \cr
} } \right)\left( {\matrix{
{30} \cr
{10} \cr
} } \right) - \left( {\matrix{
{30} \cr
1 \cr
} } \right)\left( {\matrix{
{30} \cr
{11} \cr
} } \right) + \left( {\matrix{
{30} \cr
2 \cr
} } \right)\left( {\matrix{
{30} \cr
{12} \cr
} } \right)....... + \left( {\matrix{
{30} \cr
{20} \cr
} } \right)\left( {\matrix{
{30} \cr
{30} \cr
} } \right)$$$
is where $$\left( {\matrix{ n \cr r \cr } } \right) = {}^n{C_r}$$
is where $$\left( {\matrix{ n \cr r \cr } } \right) = {}^n{C_r}$$
$$\left( {\matrix{
{30} \cr
{10} \cr
} } \right)$$
$$\left( {\matrix{
{30} \cr
{15} \cr
} } \right)$$
$$\left( {\matrix{
{60} \cr
{30} \cr
} } \right)$$
$$\left( {\matrix{
{31} \cr
{10} \cr
} } \right)$$